Assignment - Implementing a simple Collision System

Given the following interface which exposes a method  collide  which takes a non-modifiable Collidable as a parameter returns true if  caller  collides with the given  Collidable  parameter.


public interface ICollidable {

public boolean collide(ICollidable c);

}



Create a class Box and implements  ICollidable  and stores fields describing a 2D box in space.

Two boxes collide if they share some portion on the space.
This is a blurry definition, you have to come up with a more formal and mathematical description of what collision means.

 Box  must also override the  toString  method from  Object  superclass.

The following image gives you a (big) hint on how to formalize collisions in two 2D.

Pink and blue boxes are colliding while green and blue are not for instance.

Create a class Arena which stores information about a set of Collidable Objects and exposes a method with the following signatures.
 Arena  stores an array of  Collidable  which size (can be assumed) never exceed  1000  ;


public void checkCollisions(){

}

@Override
public String toString() {

}


 checkCollisions  should check for all collision between all  ICollidable  objects. On the event of a collision between two objects A and B it should print the following:

    System.out.println("Collision: " +  A.toString() + " "+ B.toString());


 toString  takes care of drawing the Arena to standard output (console). Draw the boundaries of the Area using the plus  +  , character.
Boxes must be drawn using the point  .  character and corner using the  +  character.
You can always assume that Collidable Objects coordinates are never lower than  0  or greater than  99  .

In order to test out collision detection system, you should also provide a  init  function which inits boxes randomly (within arena boundaries) and a main which will execute a demo.

    public static void main(String[] args) {
Arena a = new Arena();
a.initArena(10); //initialize arena with 10 random Box

System.out.println(a.toString()); // Print the Arena

a.checkCollisions(); // Detect collisions and print them out on stdout
}

//init arena should init boxes randomly.

public void initArena(final int NO){
Random r = new Random(System.currentTimeMillis());
objects = new Box[NO];
for(int i=0; i<NO; i++){
//function that creates a random box
Box br=createRandomBox(r,....);
objects[i] =br;
}
}


The following is the kind of result you should aim to obtain.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                   +..................................+           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .                                  .           +
+                                                   .       +....+                     .           +
+                                                   .       .    .                     .           +
+                                                   .       .    .                     .           +
+                                                   .       .    .                     .           +
+                                                   .       .    .                     .           +
+                                                   .       .    .                     .           +
+                                                   +..................................+           +
+                                                           .    .                                 +
+                                                           .    .                                 +
+                  +...........................................................+                   +
+                  .                                        +....+             .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  .                                                           .                   +
+                  +...........................................................+                   +
+                                                                                                  +
+                                                                                             +.+  +
+                                                                                             . .  +
+                                                                                             . .  +
+                                                                                             . .  +
+                                                                                             . .  +
+                                                                                             . .  +
+                                                                                             . .  +
+                                                                                             . .  +
+                                                                                             . .  +
+                +.................................................................+          . .  +
+                .                                                                 .          . .  +
+                .                                                                 .          +.+  +
+                .                                                                 .               +
+                +.................................................................+               +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
+                                                                                                  +
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Collision:  60:49-5:10  19:58-60:14
Collision:  60:49-5:10  52:10-35:45



Final Remarks

What is the complexity of the  checkCollision  method?
Do you think it can be used in a game?
Can it be used in a game, even if the number of objects is, more than 1000?